OAEP is a widely used public-key encryption scheme based on trapdoor permutations. Its security proof has been scrutinized and amended repeatedly. Fifteen years after the introduction of OAEP, we present a machine-checked proof of its security against adaptive chosen-ciphertext attacks under the assumption that the underlying permutation is partial-domain one-way. The proof can be independently verified by running a small and trustworthy proof checker and fixes minor glitches that have subsisted in published proofs. We provide an overview of the proof, highlight the differences with earlier works, and explain in some detail a crucial step in the reduction: the elimination of indirect queries made by the adversary to random oracles via the decryption oracle. We also provide—within the limits of a conference paper—a broader perspective on independently verifiable security proofs.